Skip to main content
SpringerLink
Log in

An approach for calculating correlation functions in the six-vertex model with domain wall boundary conditions

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We address the problem of calculating correlation functions in the six-vertex model with domain wall boundary conditions by considering a particular nonlocal correlation function, called the row configuration probability. This correlation function can be used as a building block for computing various (both local and nonlocal) correlation functions in the model. We calculate the row configuration probability using the quantum inverse scattering method, giving the final result in terms of multiple integrals. We also discuss the relation to the emptiness formation probability, another nonlocal correlation function, which was previously computed using similar methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Univ. Press, Cambridge (1993).

    Book  MATH  Google Scholar 

  2. V. E. Korepin, Commun. Math. Phys., 86, 391–418 (1982).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. A. G. Izergin, Dokl. Akad. Nauk SSSR, 297, 331–333 (1987).

    MathSciNet  Google Scholar 

  4. A. G. Izergin, D. A. Coker, and V. E. Korepin, J. Phys. A, 25, 4315–4334 (1992).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. F. Colomo and A. G. Pronko, SIAM J. Discrete Math., 24, 1558–1571 (2010); arXiv:0803.2697v2 [math-ph] (2008).

    Article  MathSciNet  MATH  Google Scholar 

  6. F. Colomo and A. G. Pronko, J. Stat. Phys., 138, 662–700 (2010); arXiv:0907.1264v2 [math-ph] (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. N. M. Bogoliubov, A. V. Kitaev, and M. B. Zvonarev, Phys. Rev. E, 65, 026126 (2002); arXiv:cond-mat/ 0107146v3 (2001).

    Article  MathSciNet  ADS  Google Scholar 

  8. N. M. Bogoliubov, A. G. Pronko, and M. B. Zvonarev, J. Phys. A, 35, 5525–5541 (2002); arXiv:math-ph/ 0203025v2 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. O. Foda and I. Preston, J. Stat. Mech. Theory Exp., 0411, P11001 (2004); arXiv:math-ph/0409067v1 (2004).

    Article  MathSciNet  Google Scholar 

  10. F. Colomo and A. G. Pronko, J. Stat. Mech. Theory Exp., 0505, 05010 (2005); arXiv:math-ph/0503049v2 (2005).

    Article  MathSciNet  Google Scholar 

  11. F. Colomo and A. G. Pronko, Nucl. Phys. B, 798, 340–362 (2008); arXiv:0712.1524v1 [math-ph] (2007).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. K. Motegi, Phys. A, 390, 3337–3347 (2011); arXiv:1101.0187v3 [math-ph] (2011).

    Article  MathSciNet  Google Scholar 

  13. P. Di Francesco and N. Reshetikhin, Commun. Math. Phys., 309, 87–121 (2012); arXiv:0908.1630v1 [math-ph] (2009).

    Article  ADS  MATH  Google Scholar 

  14. I. Fischer and D. Romik, Adv. Math., 222, 2004–2035 (2009); arXiv:0903.5073v2 [math.CO] (2009).

    Article  MathSciNet  MATH  Google Scholar 

  15. L. A. Takhtadzhyan and L. D. Faddeev, Russ. Math. Surveys, 34, 11–68 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  16. A. G. Izergin, V. E. Korepin, and N. Yu. Reshetikhin, J. Phys. A, 20, 4799–4822 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  17. R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Acad. Press, London (1982).

    MATH  Google Scholar 

  18. N. Kitanine, J.-M. Maillet, and V. Terras, Nucl. Phys. B, 554, 647–678 (1999); arXiv:math-ph/9907020v1 (1999).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. L. Fischer, Adv. Appl. Math., 37, 249–267 (2006); arXiv:math/0501102v1 (2005).

    Article  MATH  Google Scholar 

  20. G. Szegö, Orthogonal Polynomials (Colloq. Publ., Vol. 23, 4th ed.), Amer. Math. Soc., Providence, R. I. (1975).

    MATH  Google Scholar 

  21. P. Zinn-Justin, Phys. Rev. E, 62, 3411–3418 (2000); arXiv:math-ph/0005008v2 (2000).

    Article  MathSciNet  ADS  Google Scholar 

  22. P. Zinn-Justin and Ph. Di Francesco, Theor. Math. Phys., 154, 331–348 (2008).

    Article  MATH  Google Scholar 

  23. D. Zeilberger, “Proof of a conjecture of Philippe Di Francesco and Paul Zinn-Justin related to the qKZ equation and to Dave Robbins” two favorite combinatorial objects,” http://www.math.rutgers.edu/~zeilberg/ mamarim/mamarimhtml/diFrancesco.html (2007).

  24. C. A. Tracy and H. Widom, Commun. Math Phys., 279, 815–844 (2008); Erratum, 304, 875–878 (2011); arXiv:0704.2633v3 [math.PR] (2007).

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INFN, Sezione di Firenze, Firenze, Italy

    F. Colomo

  2. St. Petersburg Department of the Steklov Institute of Mathematics, RAS, St. Petersburg, Russia

    A. G. Pronko

Authors
  1. F. Colomo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. G. Pronko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Colomo.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 171, No. 2, pp. 254–270, May, 2012.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colomo, F., Pronko, A.G. An approach for calculating correlation functions in the six-vertex model with domain wall boundary conditions. Theor Math Phys 171, 641–654 (2012). https://doi.org/10.1007/s11232-012-0061-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-012-0061-2

Keywords

Search

Navigation